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The phrase "a complex task that" is correct and usable in written English.
You can use it when describing a specific task that involves multiple components or challenges.
Example: "Completing the project on time is a complex task that requires careful planning and coordination among team members."
Alternatives: "a challenging task that" or "a difficult task that".
Exact(59)
Earthquakes exert lateral as well as vertical forces, and a structure's response to their random, often sudden motions is a complex task that is just beginning to be understood.
The procurement of military manpower is in itself a complex task that includes the calling up of reserves; the induction of large numbers of raw recruits; and the allocation of manpower to the army, navy, and air force and, within these major components, to the respective arms, services, and other subdivisions.
It is a complex task that was tackled with different learning algorithms implemented in Weka.
Design of diagnosis systems is a complex task that involves many different steps.
Landscape protection planning is a complex task that requires an integrated assessment and involves heterogeneous issues.
Designing user interfaces is a complex task that needs to be supported by appropriate design guides.
The simulation of engineering problems is quite often a complex task that can be time consuming.
Gastrointestinal endoscopy is a complex task that involves an interaction of cognitive and manual skills.
Providing mediation is a complex task that requires effort; the mediator must pay full attention to the interaction.
Therefore, the selection of materials can be a complex task that requires great academic knowledge and practical experience.
Programming heterogeneous systems efficiently is a complex task, that often requires the use of specific programming environments.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com